Heisenberg's S-matrix program and Feynman's divergence problem

• URL: http://arxiv.org/abs/2511.02847v1
• Date: Fri, 24 Oct 2025 10:58:49 GMT
• Title: Heisenberg's S-matrix program and Feynman's divergence problem
• Abstract summary: We regularize all terms of the scattering operator's approximations using the deviation factor.<n>We provide a positive answer to the well-known problem of J. R. Oppenheimer regarding scattering operators in QED.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: In the present article, we assume that the first approximation of the scattering operator is given and that it has the logarithmic divergence. This first approximation allows us to construct the so called deviation factor. Using the deviation factor, we regularize all terms of the scattering operator's approximations. The infrared and ultraviolet cases as well as concrete examples are considered. Thus, for a wide range of cases, we provide a positive answer to the well-known problem of J. R. Oppenheimer regarding scattering operators in QED: ``Can the procedure be freed of the expansion in $\varepsilon$ and carried out rigorously?"

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